Background: Analysis of genomes evolving via block-interchange events leads to a combinatorial problem of sorting by block-interchanges, which has been studied recently to evaluate the evolutionary relationship in distance between two biological species since block-interchange can be considered as a generalization of transposition. However, for genomes consisting of multiple chromosomes, their evolutionary history should also include events of chromosome fusions and fissions, where fusion merges two chromosomes into one and fission splits a chromosome into two. Results: In this paper, we study the problem of genome rearrangement between two genomes of circular and multiple chromosomes by considering fusion, fission and block-interchange events altogether. By use of permutation groups in algebra, we propose an (n2) time algorithm to efficiently compute and obtain a minimum series of fusions, fissions and block-interchanges required to transform one circular multi-chromosomal genome int...